Question

if the mean gpa among students is 3.00 with a standard deviation of 1.5, what is the probability that a random sample of 100 students will have a mean gpa greater than 3.20?

round to 4 decimal places

Answer 1

Given

=3.00

=1.5

Now calculate p(x>3.20) if n =100

P(x > 3.20) = 0.5 - p(0 < z < x-/(/n)

= 0.5 - p(0 < z < 3.20-3/(1.5/100)

= 0.5 - p(0 < z < 1.33)

= 0.5 - 0.4082

P(x > 3.20) = 0.0918

Therefore the probability of GPA greater than 3.20 is 0.0918.